I really had to read through this whole thread to grasp what was going on with critical strike and what it actually does. ,

So in simple terms PC initiates an attack
There is a critical strike skill check
If that skill check is successful, a bonus is added to the hit probability
The attack is compared to the defence of the opponent
If the attack is successful normal damage is applied

The one thing I am not clear on is how the to hit bonus is calculated.

I really had to read through this whole thread to grasp what was going on with critical strike and what it actually does. ,

So in simple terms PC initiates an attack
There is a critical strike skill check
If that skill check is successful, a bonus is added to the hit probability
The attack is compared to the defence of the opponent
If the attack is successful normal damage is applied

The one thing I am not clear on is how the to hit bonus is calculated.

I just want to know why dodging was considered bugged, but this wasn't. Even though dodging resulted in a penalty, they both seem to be missing part of their formula.

My understanding is that Dodging actually had a formula that clearly intended the described behavior, but some minor error (a single digit or whatever those mad smart coding nerds talk about) was off. On the other hand, Critical Strike's formula never included anything related to damage to begin with. It could be argued back and forth all year about what the in-game description said, what logic says, what other games do, etc. etc., but although I would agree "Critical Strike" intuitively "should" probably add to damage, it's been clearly decided to be beyond the scope of DFU to change how the classic coding was done.

I'm going to move on to other topics now... kind of worn out on this one.

Only the Bethesda developers could even attempt to explain how this skill was developed, the intent behind it, how it was implemented then adjusted, and it is likely no one would be able to without some kind of documentation. What we can say for sure is by the documentation that is available it doesn't do what the initial intent of the skill seemed to be.

To the question you could answer yes as it does have an effect on whether you hit an enemy thus causing damage to that enemy. Does it add additional damage? I think the discussion in this thread clearly shows it does not work as many thought it did for many many years.

Is it worth taking as a primary or major skill? Well it is checked each time you swing a weapon, how my understanding of how skills and levels work in DFU each attempt at a skill adds to increasing that skill. The formula I have heard to get a level is all 3 of your primary skills have input, the top 2 of your major have input, and the top one of your minor has input. You need to get 15 skill raises spread over those 6 skills to get a level. So if you are a heavy melee user this would be a way that you could get fast increase in the skill pool. So if your intent is to get levels quickly this skill can help with that if placed in the primary, major, or minor pools.